Microstrip line discontinuities simulation at microwave frequencies
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications38Microstrip Line Discontinuities Simulation at Microwave FrequenciesDr. A.K. Rastogi1*(FIETE), (MISTE), Munira Bano1, Manisha Nigam21. Department of Physics & Electronics, Institute for Excellence in Higher Education, Bhopal, (M.P.),India-4620162. Govt. MVM, Bhopal, (M.P.), India-462008*Email:akrastogi_bpl@yahoo.comAbstractMicrowave and Millimeter wave integrated circuits (MICs) have experienced a tremendous growth over the last50 years. Microstrip line is one of the popular lines in these MICs. Due to the layout necessities, anelectromagnetic wave that propagates down a microstrip line may encounter discontinuities such as T-junctions,Bends and vias. A simulation model is presented here for analysing these discontinuities in microstrips throughSonnet Software. The parameters of microstrip lines are determined from the empirical formulae which arebased on full wave analysis. The simulation work has been performed on Alumina substrate. The discontinuitiesare simulated and compensated which gives important results for designing high frequency microwave circuits.Key Words: Microwave and millimeter wave integrated circuits (MICs), microstrip line, microstrip linediscontinuities, T-junctions, bends, steps in width, full wave analysis, substrate permittivity and sonnet software.1. IntroductionMonolithic Microwave Integrated Circuits based on Planar Transmission Lines such as microstrip are beingconsidered as viable candidates for microwave communications and other applications. The planar configurationimplies that the characteristics of the element can be determined by the dimensions in a single plane. Thecommonly used different types of printed transmission lines for MICs are microstrip line, strip line, suspendedstripline, slotline, coplanar waveguide and finline (Gupta et al. 1979). Microstrip line is one of the popular linesin transmission structures, mainly due to the fact that the mode of propagation on microstrip is almost TEM. Themicrostrip line consists of a single conductor trace on one side of a dielectric substrate and a single ground planeon its opposite side as shown in Figure 1. Since it is an open structure it features the ease of interconnections andadjustments.Methods of microstrip analysis may be classified into three groups- Quasi Static Methods, Dispersion Methodsand Full Wave Analysis. In Quasi Static Methods, the nature of the mode of propagation is considered to be pureTEM, and microstrip characterizations are calculated from the electrostatic capacitance of the structure. It isfound from analysis, that this method is adequate for designing circuits at lower frequencies (below X-band)where the strip width and substrate thickness are much smaller than the wavelength in the dielectric material. Inthe second group, called dispersion models, the deviation from the TEM nature is accounted for quasiempirically. The methods in the third group, take into account the hybrid nature of mode of propagation i.e.quasi TEM mode of propagation (Bhat & Koul 1980; Fooks & Zakarevicius 1990).2. Microstrip SynthesisIn actual design of microstrip, one wishes to determine the width ‘w’ required to obtain specified characteristicimpedance ‘Z0’ on a substrate of known permittivity ‘εr’ and thickness ‘h’. This operation is called synthesis.Various researchers have reported formulas for microstrip calculations (Wheeler 1964; 1965). Owens (1976),carefully investigated the ranges of applicability of many of the expressions given by Wheeler, comparingcalculated results with numerical computations. The closed formulas are highly desirable as they are accurateand fast. CAD algorithms can be implemented with these formulas of Edward & Steer.2.1 Synthesis FormulaFor given Z0 and frequency:In case of narrow strips i.e. whenZ0 > (44 - εr) Ω1exp418exp−−=HHhw...… (1)Where++−++=πεπεεε 4ln12ln11219.119)1(20rrrrZH …… (2)
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications39and24ln12ln1121121−++−−+=πεπεεεεrrrreffH…… (3)whereH is given by equation (2) or alternatively as a function ofhwfrom equation (1)++= 2164ln2whwhH …… (4)For microstrip line on Alumina ),10( =rε this expression appears to be accurate to 2.0± % over theimpedance range Ω≤≤ 508 0Zwhenhwand rε are given:+++= 2164ln)1(29.11920whwhZrε…. (5)3. Microstrip DiscontinuitiesAll practical distributed circuits, whether in waveguides, coaxial lines or any other propagation structure, mustinherently contain discontinuities. A straight uninterrupted length of transmission structure would be of littleengineering use, and in any case junctions are essential. Although such discontinuities give rise to only verysmall capacitances and inductances (often <0.1pF and <0.1nH) the reactance of these become particularlysignificant at the high microwave and millimetre wave frequencies. The performance of amplifiers for examplehas been shown to be considerably affected by microstrip discontinuity. Many other circuits such as filters,mixers and oscillators involve several discontinuities. All technologies whether based on hybrid MIC or MMICinherently involves transmission discontinuities (Wheeler 1977). Discontinuity modelling is based uponequivalent capacitances and inductances. Discontinuity capacitance evaluation has been performed by Silvester& Benedek (1973) and discontinuity inductance evaluation has been performed by Gupta & Gopinath (1977).The following are several forms of discontinuities emerging from circuit requirements:a) Open circuitsb) Series coupling gapsc) Short circuits through to the ground planed) Step width changese) T & Cross junctions3.1 Microstrip BendsA microstrip bend may be formed by two lines of equal or unequal impedances and is normally used forintroducing flexibility in the layout of the circuit design. The equivalent circuit of the microstrip bend with linesof equal impedance is shown in the Figure 2.In practical circuits, microstrip bends are chamfered to compensate the excess capacitance.3.2 T-junctionsThe T-junctions is perhaps the most important discontinuity in a microstrip as it is found in most circuits such asimpedance networks, stub filters and branch line couplers. A microstrip T-junction and its equivalent circuit areshown in the Figure 3. The discontinuity capacitance for this structure has been calculated by Silvester &Benedek (1973).The T-junction discontinuity compensation is much more difficult than right angled bends and steps in widthdiscontinuity compensation techniques. The T-junctions can be compensated by adjusting the lengths of the threemicrostrip lines forming the junction.3.3 Steps in WidthThere exists step discontinuity at junctions of two microstrip lines that have different impedances. This type ofdiscontinuity is encountered when designing matching transformers, couplers and filters. The configurations ofstep discontinuity and its equivalent circuit are shown in the Figure 4. Results for excess capacitance have beengiven by Farrar & Adams (1971), Benedek & Silvester (1972) and Gupta & Gopinath (1977).
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications40The compensation in this case is done to reduce the effect of discontinuity reactances by chamfering the largewidth.4. Results & DiscussionFigure 5. (a) & (b) shows the two and three dimensional model for microstrip bend respectively while the Figure6. (a) & (b) shows simulation model of T-junctions and Steps in width through Sonnet Software simulationrespectively, which is performed on Alumina substrate of substrate permittivity εr=9.8 and loss tangenttanδ=0.0002 and substrate thickness h=0.5 mm. The synthesis equation gives the proper width ‘w’ and effectivedielectric constant ‘εeff’ required for simulating the microstrip discontinuities.SONNET Software is commercial Software which provides solutions for high frequency electromagneticanalysis. This Em simulation software is used for design and analysis for high frequency microstrip circuits. Theanalysis engine of Sonnet Suite®, Em is appropriate for a wide range of 3D planar structures. The via capabilitiesallow the analysis of air bridges, wire bonds, spiral inductors, wafer probes, and internal ports as well as forsimple grounding.All the three discontinuities are chamfered in different ways in order to compensate the excess reactance. Thediscontinuities and their compensated models are analysed which are shown in the Figure 7. (a), (b) and (c). TheS-parameters gives us a way of representing a networks transmission and reflection coefficients as they are theonly parameters that can be measured at high frequencies.The results are shown in the Figure 8, 9 and 10 through graphs of the reflection and transmission coefficients.Figure 8. (a) shows clearly that when the right angled bend is chamfered by changing the angle from 90° to 45°,the transmission is increased through the line and the reflection is decreased which is shown in the Figure 8 (b).Figure 9. (a) & (b) shows that when the microstrip T-junction discontinuity is compensated by increasing thewidth of the junction, the transmission and reflection both becomes better.Figure 10. (a) & (b) shows that compensating the Step in Width by chamfering it, the reflection and transmissionare enhanced at the higher frequencies esp. above 10 GHz.5. ConclusionMicrostrip lines are considered as viable candidates for MMICs. Microstrip due to its various design advantagesis particularly very attractive. A straight uninterrupted length of waveguide or transmission line would be of littleengineering use. Simulation model is presented in this paper for analysing the general discontinuities inmicrostrips at higher frequencies. The discontinuities are finely modelled through simulation which shows thatthe compensated models are better than the uncompensated ones as they increase the transmission and decreasethe reflection. The results given here have been applied to most commonly used substrate. The results presentedhere are useful in the design of MMICs and they form a basis for the improvement of existing CAD models.References:Benedek, P. & Silvester, P. (1972), “Equivalent Capacitance for Microstrip Gaps and Steps”, IEEE Trans.Microwave Theory Tech. MTT-20, 729-733.Bhat, B. & Koul, S.K. (1980), “Stripline-like Transmission Lines for Microwave Integrated Circuits”, WileyEastern Limited, New-Delhi.Edwards, T.C. & Steer, M.B. “Foundations of Inter-connect and Microstrip Design”, John Wiley & Sons Ltd.Farrar, A. & Adams, A.T. (1971), “Computation of Lumped Microstrip Capacitances by Matrix Methods:Rectangular Sections and End Effect”, IEEE Trans. Microwave Theory Tech. MTT-19, 495-497.Fooks, E.H. & Zakarevicius, R.A. (1990), “Microwave Engineering using Microstrip Circuits”, Prentice Hall ofAustralia.Gupta, K.C., Garg, R. & Bahl, I.J. (1979), “Microstrip Lines and Slot Lines”, Artech House Inc., Washington.Gupta, K.C., & Gopinath, A. (1977), “Equivalent Circuit Capacitance of Microstrip Step Change in Width”,IEEE Trans. Microwave Theory Tech. MTT-25, 819-822.Owens, R.P. (1976), “Accurate Analytical Determination of Quasi-static Microstrip Line Parameters,” The Radioand Electronic Engineer 46, 360-364.Silvester, P. & Benedek, P. (1973), “Microstrip Discontinuity Capacitances for Right-angle Bends, T-junctionsand Crossing”, IEEE Trans. Microwave Theory Tech. MTT-21, 341-346.Wheeler, H.A. (1964), “Transmission-line Properties of Parallel Wide Strips by a Conformal MappingApproximation”, IEEE Trans. Microwave Theory and Tech. 12, 280-289.Wheeler, H.A. (1965), “Transmission-line Properties of Parallel Strips separated by a Dielectric Sheet,” IEEETrans. Microwave Theory and Tech.13, 172-185.Wheeler, H.A. (1977), “Transmission Line Properties of a Strip on a Dielectric Sheet on a plane”, IEEE Trans.MTT-25, 631-647.
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications41Figure 1. Cross Sectional View of Microstrip lineFigure 2. Microstrip Bend Geometry and its Equivalent CircuitFigure 3. Microstrip T-junction and its Equivalent CircuitFigure 4. Microstrip Step Discontinuity and its Equivalent Circuit
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications42Figure 5(a). Microstrip Bend through SonnetFigure 5(b). 3D Microstrip Bend
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications43Figure 6(a). Microstrip T-junction through SonnetFigure 6 (b). Microstrip Step in Width through Sonnet
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications44Figure 7(a). Compensated model of Microstrip Bend DiscontinuityFigure 7(b). Compensated model of Microstrip T-junction Discontinuity
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications45Figure 7(c). Compensated model of Microstrip Step in WidthFigure 8(a). Transmission Coefficient Vs Frequency for Microstrip Right angledBend and Compensated Bend.
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications46Figure 8(b). Reflection Coefficient Vs Frequency for Microstrip Right angledBend and Compensated Bend .Figure 9(a). Transmission Coefficient Vs Frequency for Microstrip T-junctionand Compensated T-junction.
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications47Figure 9(b). Reflection Coefficient Vs Frequency for Microstrip T-junctionand Compensated T-junction.Figure 10(a). Transmission Coefficient Vs Frequency for Microstrip StepDiscontinuity and Compensated Step in Width.
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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications48Figure 10(b). Reflection Coefficient Vs Frequency for Microstrip StepDiscontinuity and Compensated Step in Width.
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